Considering the positions involved I would certainly 4bet and call here. He knows your BTN range is weak so he will 3bet weaker hands; that means we can profitably 4bet and get it in preflop (mind that if you or him were on early positions that changes it all).

Once you called, why did you call? To get a favourable flop, right? So there you go, an (almost) perfect flop for your ladies. It doesn't make sense to fold there.

He might go all in with a T (like AT), with JJ, with A
K
/A
Q
and so many other hands you beat!

Plus, I think if he had AA, KK or TT he wouldn't go all in all the sudden and would bet smaller to induce you to call.

Of course he can show up there sometimes with hands that beat you but hey, that's poker. You can't be 100% sure all the time when the money goes in; if you consider his whole range, you're crushing him on this flop.

Finally, if he does have AA, he didn't win the hand. It's actually a tie. Why? Because next time you will have the AA, your opponent will have the QQ and you will go all in all the same. Money comes and goes but no one actually wins money on those "coolers". But if your opponent had JJ or AT, you let go the opportunity to get some of his $, because you wouldn't do the same if you were the one with AT, right?